Multi-strand steel cords must have a durable resistance to corrosion with a view to increasing their life span. Corrosion attack of the cords can be avoided not only by providing a suitable coating such as zinc but also by proper constructional features which allow rubber to penetrate between the individual steel filaments in the cord. Rubber penetration can be obtained by providing free spaces between the individual filaments. The situation with multi-strand steel cords is, however, not that simple as is the case with single-strand steel cords for the reinforcement of passenger or truck tires. A typical example of a multi-strand steel cord is a 7.times.19-construction. This steel cord has 133 individual steel filaments. Protecting every filament against corrosion attack means that every filament, even the center filaments of the core strand, should be enveloped with a rubber layer. As a consequence, relatively large spaces must be provided between neighbouring filaments. When providing large spaces between the filaments, however, the strands building up the cord and/or the cord structure itself loose their compact and uniform geometrical shape during embedment and, as a consequence, the cord no longer offers a uniform reinforcing level along its length. Moreover, it is always required that a certain given reinforcement level is achieved with the smallest possible volume of reinforcing material. This means that for a predetermined breaking load, the cross-sectional area of the steel cord should be as small as possible, which means that the outer diameter of each cord should be choosen as small as possible for a given steel section. It goes without saying that this requirement contravenes the above stated aim of providing relatively large spaces between neighbouring filaments in the cord.